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Constraining Upper-Mantle Deformation Patterns from Bayesian Inversion of Surface Waves J Geodynamic tomography: constraining upper-mantle deformation patterns from Bayesian inversion of surface waves J. K. Magali, T Bodin, N Hedjazian, H Samuel, S Atkins To cite this version: J. K. Magali, T Bodin, N Hedjazian, H Samuel, S Atkins. Geodynamic tomography: constraining upper-mantle deformation patterns from Bayesian inversion of surface waves. Geophysical Journal International, Oxford University Press (OUP), 2021, 224 (3), pp.2077 - 2099. 10.1093/gji/ggaa577. hal-03189035 HAL Id: hal-03189035 https://hal.archives-ouvertes.fr/hal-03189035 Submitted on 2 Apr 2021 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Geophys. J. Int. (2021) 224, 2077–2099 doi: 10.1093/gji/ggaa577 Advance Access publication 2020 December 03 GJI Seismology Geodynamic tomography: constraining upper-mantle deformation patterns from Bayesian inversion of surface waves J. K. Magali,1 T. Bodin ,1 N. Hedjazian ,1 H. Samuel 2 and S. Atkins3 1UCBL, CNRS, LGL-TPE, Universite´ de Lyon, 69622 Villeurbanne, France. E-mail: [email protected] 2Institut de Physique du Globe de Paris, Universite´ de Paris, CNRS, F-75005 Paris, France 3Laboratoire de Geologie,´ Ecole Normale Superieure,´ PSL Res. Univ, 75005 Paris, France Downloaded from https://academic.oup.com/gji/article/224/3/2077/6019874 by INFU BIBLIO PLANETS user on 02 April 2021 Accepted 2020 December 1. Received 2020 November 21; in original form 2020 September 23 SUMMARY In the Earth’s upper mantle, seismic anisotropy mainly originates from the crystallographic preferred orientation (CPO) of olivine due to mantle deformation. Large-scale observation of anisotropy in surface wave tomography models provides unique constraints on present- day mantle flow. However, surface waves are not sensitive to the 21 coefficients of the elastic tensor, and therefore the complete anisotropic tensor cannot be resolved independently at every location. This large number of parameters may be reduced by imposing spatial smoothness and symmetry constraints to the elastic tensor. In this work, we propose to regularize the tomographic problem by using constraints from geodynamic modelling to reduce the number of model parameters. Instead of inverting for seismic velocities, we parametrize our inverse problem directly in terms of physical quantities governing mantle flow: a temperature field, and a temperature-dependent viscosity. The forward problem consists of three steps: (1) calculation of mantle flow induced by thermal anomalies, (2) calculation of the induced CPO and elastic properties using a micromechanical model, and (3) computation of azimuthally varying surface wave dispersion curves. We demonstrate how a fully nonlinear Bayesian inversion of surface wave dispersion curves can retrieve the temperature and viscosity fields, without having to explicitly parametrize the elastic tensor. Here, we consider simple flow models generated by spherical temperature anomalies. The results show that incorporating geodynamic constraints in surface wave inversion help to retrieve patterns of mantle deformation. The solution to our inversion problem is an ensemble of models (i.e. thermal structures) representing a posterior probability, therefore providing uncertainties for each model parameter. Key words: Inverse theory; Probability distributions; Seismic anisotropy; Seismic tomog- raphy; Surface wave and free oscillations. seismic data, tomographers have produced detailed models of az- 1 INTRODUCTION imuthal anisotropy (e.g. Debayle et al. 2005; Deschamps et al. Seismic anisotropy reveals key insights into the Earth’s interior 2008; Adam & Lebedev 2012; Yuan & Beghein 2013, 2014), and structure and dynamics. In the upper mantle, the propagation of radial anisotropy (e.g., Plomerova´ et al. 2002;Lebedevet al. 2006; seismic waves appears to be anisotropic, which has generally been Nettles & Dziewonski´ 2008; Chang et al. 2014, 2015). Numerous associated with the preferred alignment of mantle minerals (Nico- studies have inverted dispersion curves by minimizing the differ- las & Christensen 1987; Montagner 1994). This so-called intrinsic ence between observed and synthetic phase and/or group velocities, anisotropy relates to the strain history induced by regional-scale proving that they can effectively constrain the depth dependence convection and is observable with various seismological tools, in- of anisotropy (e.g., Montagner & Tanimoto 1990; Ritzwoller et al. cluding surface waves. 2002). Seismic anisotropy can be described with 21 independent com- ponents of the elastic tensor. In practice however, the full tensor 1.1 Surface wave tomography studies cannot be resolved by the seismic data independently at every lo- Surface wave tomography offers a powerful technique to constrain cation, and generally only a restricted number of parameters are seismic anisotropy and to image the structure of the upper man- inverted for. This is done by assuming specific symmetry classes, tle at both regional and global scales. With growing amounts of or by using petrological constraints to impose relations between C The Author(s) 2020. Published by Oxford University Press on behalf of The Royal Astronomical Society. All rights reserved. For permissions, please e-mail: [email protected] 2077 2078 J.K. Magali et al. some of the parameters. Surface waves in particular are only sensi- Ritzwoller 2002;Shenet al. 2012; Bodin et al. 2016; Ravenna & tive to 13 parameters that are just a linear combination of the elastic Lebedev 2017;Xu&Beghein2019). constants (Montagner & Nataf 1986). General practices in surface In this study, we propose a complementary approach to estimate wave tomography thus investigate: (1) radial anisotropy (assuming the full elastic tensor. This involves the incorporation of geodynamic vertical transverse isotropy, VTI, where the axis of hexagonal sym- and mineral physics modelling constraints: the textural evolution of metry is vertical), constrained by comparing the speed of Rayleigh peridotite aggregates during their deformation in the convective waves with that of Love waves, also known as the Rayleigh–Love mantle. We propose a method to invert directly for the temperature discrepancy (Babuska & Cara 1991); or (2) azimuthal anisotropy, field that produces convective flow and texture evolution. Modelling which deals with first-order variations of velocities as function of intrinsic anisotropy in this way removes the issue of low sensitivity the azimuth of propagation. For example, azimuthal anisotropy can from seismic waves since the elastic tensor is not explicitly inverted be inferred from the azimuthal terms of the Rayleigh wave phase for, but instead computed directly from texture evolution models. velocities (Smith & Dahlen 1973). Additionally,the inversion is performed using a Bayesian sampling Downloaded from https://academic.oup.com/gji/article/224/3/2077/6019874 by INFU BIBLIO PLANETS user on 02 April 2021 Simultaneous interpretations of radial and azimuthal anisotropy algorithm, hence provide uncertainties on the obtained temperature have been the subject of extensive research (e.g. Beghein et al. field. 2014; Burgos et al. 2014). Joint efforts involving the use of apriori information have already been conducted to reduce the high dimen- sionality of anisotropic inversion. Montagner & Anderson (1989) showed that correlations exist between the elastic constants de- 1.2 Deformation-induced seismic anisotropy rived from petrological models, thereby reducing the total number In the upper mantle, the existence of large-scale anisotropy ap- of free parameters to be inverted for. This motivated the devel- pears to be ubiquitous in regions associated with strong deformation opment of ‘vectorial tomography’ where it involves inverting for (McKenzie 1979). Its interpretation is based on the development of seven parameters instead of 13: two angles defining the strike and crystallographic preferred orientation (CPO) in olivine aggregates dip of the symmetry axis, three coefficients defining the strength during their plastic deformation (Nicolas & Christensen 1987). Due of anisotropy and finally two isotropic coefficients (Montagner & to the physical process at its origin, seismic anisotropy can be inter- Nataf 1988; Montagner & Jobert 1988). Such a medium is also preted in terms of the strain history associated with upper-mantle known as tilted transverse isotropy (TTI) and describes the 3-D circulation. distributions of anisotropy. This further led to studies revealing Different proxies have then been utilized to interpret seismic that deformation-induced anisotropy can be described by a TTI anisotropy directly in terms of mantle flow. First-order seismic ob- medium where correlations appear to exist between P-andS-wave servations suggest that the fast axis of azimuthal anisotropy tends anisotropy (Becker et al. 2006). Such correlations can then be ex- to align with horizontal mantle flow (Ribe 1989; Becker et al. 2003, ploited to further simplify anisotropic inversion. Panning & Nolet 2014). However, this behaviour may not
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